Problem: What do the following two equations represent? $4x+y = -1$ $-5x+20y = 2$
Answer: Putting the first equation in $y = mx + b$ form gives: $4x+y = -1$ $y = -4x-1$ Putting the second equation in $y = mx + b$ form gives: $-5x+20y = 2$ $20y = 5x+2$ $y = \dfrac{1}{4}x + \dfrac{1}{10}$ The slopes are negative inverses of each other, so the lines are perpendicular.